Visual Analysis of Dynamics Behaviour of an Iterative Method Depending on Selected Parameters and Modifications
There is a huge group of algorithms described in the literature that iteratively find solutions of a given equation. Most of them require tuning. The article presents root-finding algorithms that are based on the Newton–Raphson method which iteratively finds the solutions, and require tuning. The mo...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2020-07-01
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| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/22/7/734 |
| _version_ | 1797563459980754944 |
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| author | Ireneusz Gościniak Krzysztof Gdawiec |
| author_facet | Ireneusz Gościniak Krzysztof Gdawiec |
| author_sort | Ireneusz Gościniak |
| collection | DOAJ |
| description | There is a huge group of algorithms described in the literature that iteratively find solutions of a given equation. Most of them require tuning. The article presents root-finding algorithms that are based on the Newton–Raphson method which iteratively finds the solutions, and require tuning. The modification of the algorithm implements the best position of particle similarly to the particle swarm optimisation algorithms. The proposed approach allows visualising the impact of the algorithm’s elements on the complex behaviour of the algorithm. Moreover, instead of the standard Picard iteration, various feedback iteration processes are used in this research. Presented examples and the conducted discussion on the algorithm’s operation allow to understand the influence of the proposed modifications on the algorithm’s behaviour. Understanding the impact of the proposed modification on the algorithm’s operation can be helpful in using it in other algorithms. The obtained images also have potential artistic applications. |
| first_indexed | 2024-03-10T18:43:58Z |
| format | Article |
| id | doaj.art-d8b6d3e2d2114ea6b8073813ca34ba6d |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T18:43:58Z |
| publishDate | 2020-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-d8b6d3e2d2114ea6b8073813ca34ba6d2023-11-20T05:40:54ZengMDPI AGEntropy1099-43002020-07-0122773410.3390/e22070734Visual Analysis of Dynamics Behaviour of an Iterative Method Depending on Selected Parameters and ModificationsIreneusz Gościniak0Krzysztof Gdawiec1Institute of Computer Science, University of Silesia, Bȩdzińska 39, 41–200 Sosnowiec, PolandInstitute of Computer Science, University of Silesia, Bȩdzińska 39, 41–200 Sosnowiec, PolandThere is a huge group of algorithms described in the literature that iteratively find solutions of a given equation. Most of them require tuning. The article presents root-finding algorithms that are based on the Newton–Raphson method which iteratively finds the solutions, and require tuning. The modification of the algorithm implements the best position of particle similarly to the particle swarm optimisation algorithms. The proposed approach allows visualising the impact of the algorithm’s elements on the complex behaviour of the algorithm. Moreover, instead of the standard Picard iteration, various feedback iteration processes are used in this research. Presented examples and the conducted discussion on the algorithm’s operation allow to understand the influence of the proposed modifications on the algorithm’s behaviour. Understanding the impact of the proposed modification on the algorithm’s operation can be helpful in using it in other algorithms. The obtained images also have potential artistic applications.https://www.mdpi.com/1099-4300/22/7/734root findingdynamicsiterationsvisualisation |
| spellingShingle | Ireneusz Gościniak Krzysztof Gdawiec Visual Analysis of Dynamics Behaviour of an Iterative Method Depending on Selected Parameters and Modifications Entropy root finding dynamics iterations visualisation |
| title | Visual Analysis of Dynamics Behaviour of an Iterative Method Depending on Selected Parameters and Modifications |
| title_full | Visual Analysis of Dynamics Behaviour of an Iterative Method Depending on Selected Parameters and Modifications |
| title_fullStr | Visual Analysis of Dynamics Behaviour of an Iterative Method Depending on Selected Parameters and Modifications |
| title_full_unstemmed | Visual Analysis of Dynamics Behaviour of an Iterative Method Depending on Selected Parameters and Modifications |
| title_short | Visual Analysis of Dynamics Behaviour of an Iterative Method Depending on Selected Parameters and Modifications |
| title_sort | visual analysis of dynamics behaviour of an iterative method depending on selected parameters and modifications |
| topic | root finding dynamics iterations visualisation |
| url | https://www.mdpi.com/1099-4300/22/7/734 |
| work_keys_str_mv | AT ireneuszgosciniak visualanalysisofdynamicsbehaviourofaniterativemethoddependingonselectedparametersandmodifications AT krzysztofgdawiec visualanalysisofdynamicsbehaviourofaniterativemethoddependingonselectedparametersandmodifications |